On the Optimal Linear Convergence Rate of a Generalized Proximal Point Algorithm

The proximal point algorithm (PPA) has been well studied in the literature. In particular, its linear convergence rate has been studied by Rockafellar in 1976 under certain condition. We consider a generalized PPA in the generic setting of finding a zero point of a maximal monotone operator, and show that the condition proposed by Rockafellar can also sufficiently ensure the linear convergence rate for this generalized PPA. Indeed we show that these linear convergence rates are optimal. Both the exact and inexact versions of this generalized PPA are discussed. The motivation to consider this generalized PPA is that it includes as special cases the relaxed versions of some splitting methods that are originated from PPA. Thus, linear convergence results of this generalized PPA can be used to better understand the convergence of some widely used algorithms in the literature. We focus on the particular convex minimization context and specify Rockafellar's condition to see how to ensure the linear convergence rate for some efficient numerical schemes, including the classical augmented Lagrangian method proposed by Hensen and Powell in 1969 and its relaxed version, the original alternating direction method of multipliers (ADMM) by Glowinski and Marrocco in 1975 and its relaxed version (i.e., the generalized ADMM by Eckstein and Bertsekas in 1992). Some refined conditions weaker than existing ones are proposed in these particular contexts.Comment: 22 pages, 1 figur

Anti-dark and Mexican-hat solitons in the Sasa-Satsuma equation on the continuous wave background

In this letter, via the Darboux transformation method we construct new analytic soliton solutions for the Sasa-Satsuma equation which describes the femtosecond pulses propagation in a monomode fiber. We reveal that two different types of femtosecond solitons, i.e., the anti-dark (AD) and Mexican-hat (MH) solitons, can form on a continuous wave (CW) background, and numerically study their stability under small initial perturbations. Different from the common bright and dark solitons, the AD and MH solitons can exhibit both the resonant and elastic interactions, as well as various partially/completely inelastic interactions which are composed of such two fundamental interactions. In addition, we find that the energy exchange between some interacting soliton and the CW background may lead to one AD soliton changing into an MH one, or one MH soliton into an AD one.Comment: 12 pages, 6 figure

Efficient Online Quantum Generative Adversarial Learning Algorithms with Applications

The exploration of quantum algorithms that possess quantum advantages is a central topic in quantum computation and quantum information processing. One potential candidate in this area is quantum generative adversarial learning (QuGAL), which conceptually has exponential advantages over classical adversarial networks. However, the corresponding learning algorithm remains obscured. In this paper, we propose the first quantum generative adversarial learning algorithm-- the quantum multiplicative matrix weight algorithm (QMMW)-- which enables the efficient processing of fundamental tasks. The computational complexity of QMMW is polynomially proportional to the number of training rounds and logarithmically proportional to the input size. The core concept of the proposed algorithm combines QuGAL with online learning. We exploit the implementation of QuGAL with parameterized quantum circuits, and numerical experiments for the task of entanglement test for pure state are provided to support our claims

Pseudo-goldstino and electroweakinos via VBF processes at LHC

The multi-sector SUSY breaking predicts pseudo-goldstino which can couple to the visible sector more strongly than the ordinary gavitino and thus induce the decays of the lightest neutralino and chargino (collectively called electroweakinos) inside the detector. In this note we study the electroweakino pair productions via vector boson fusion (VBF) processes followed by decays to pseudo-goldstino at the LHC. Our Monte Carlo simulations show that at the 14 TeV LHC with 3000 fb^{-1} luminosity the dominant production channel pp->chargino+neutralino+2 jets can have a statistical significance above 2-sigma while other production channels are not accessible.Comment: Version in JHEP (comments added

Control, Conformity and Contradiction: Changes in Chinese Language and Literacy (Yuwen) Curriculum from 1980-2010 in China

Inspired by the researcher’s observations of and queries in the language curriculum as a practicing teacher for the past 20 years, this thesis addresses how the high school Chinese language and literacy (Yuwen) curriculum in China is controlled and directed by the social and political dominations from 1980 to 2010 and how the teachers and schools respond to the top-down curriculum change in their teaching practice. This research project fills a research gap of the lack of a systematic study of the Chinese language and literacy curriculum in Western scholarship by conducting an in-depth analysis of the relevant syllabuses, textbooks and teachers’ responses to the curriculum change in China. In doing so, this thesis attempts to achieve two theoretical implications: 1) A test of applicability of the existing literacy and other social theories originated in the Western developed countries to the Chinese context; 2) An empirical study that examines the data obtained in China with a view to enriching and complementing the existing literacy theories. This project is also expected to have impact on the policy makers in China and beyond, like in Australia and the USA where Chinese migrants and international students constitute a substantial learning population